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Search: id:A103971
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| A103971 |
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Expansion of (1-sqrt(1-4x-16x^2))/(2x). |
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+0
2
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| 1, 5, 10, 45, 190, 930, 4660, 24445, 131190, 719830, 4013260, 22684370, 129661740, 748252580, 4353379560, 25508284445, 150392391590, 891549228430, 5310994644060, 31775749689670, 190860711108740, 1150473009844380
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Image of c(x), the g.f. of the Catalan numbers A000108 under the mapping g(x)->(1+4x)g(x(1+4x)). In general, the image of the Catalan numbers under the mapping g(x)->(1+i*x)g(x(1+i*x)) is given by a(n)=sum{k=0..n, i^(n-k)C(k)C(k+1,n-k)}.
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FORMULA
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G.f. : (1-sqrt(1-4x(1+4x))/(2x); a(n)=sum{k=0..n, 4^(n-k)C(k)C(k+1, n-k)}.
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CROSSREFS
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Sequence in context: A136138 A122173 A083515 this_sequence A035406 A103932 A034190
Adjacent sequences: A103968 A103969 A103970 this_sequence A103972 A103973 A103974
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 23 2005
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